f(x) = tan(x) ^ arctan(x)

Find f'(x).

Question

f(x) = tan(x) ^ arctan(x)

Find f'(x).

anonymous · Answer

$$f(x) = (\tan x)^{\arctan x}$$

anonymous · Answer

believe the only function that acts as its own inverse (i.e. f^-1(x) = f(x)) is y = x.

anonymous · Answer

did i help at all?

anonymous · Answer

not really, the answer in the back of the book is ridiculously long

baldymcgee6 · Answer

http://gyazo.com/83c8c62b3f1098672c155d554aee7da2

anonymous · Answer

u have to take logarithm of both sides and then u get ln(f(x))=arctan(x)ln(tanx)
 is it f'(x)= tan(x) ^ arctan(x)((ln(tanx)/(1+x^2)) + (arctanx)((sec^2x)/(tanx))))
=tan(x) ^ arctan(x)(  ln(tanx)/(1+x^2) + (arctanx)(secx)(cosecx) )

anonymous · Answer

The final answer anded up being $$f'(x) = tanx ^{arctanx}\left( \frac{ lntanx }{ 1+x^2 } + arctanxcotxsec^2x\right)$$
Thanks!

anonymous · Answer

welcome i hope u understand that (arctanx)(secx)(cosecx) =(arctanx)(sec^2x)(cotx)